A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. What is the solution to the system of equations?
Answer:
The solution to the system of equations is x = 4 and y = 2.
Step-by-step explanation:
From statement we know that the first line is [tex]y = 0.5\cdot x[/tex]. The second line is determined by knowing two distinct points and solving the resulting system of equations by definition of the equation of the line:
[tex](x_{1},y_{1}) = (3,1)[/tex] and [tex](x_{2}, y_{2}) =(-5,-7)[/tex]
[tex]3\cdot m + b = 1[/tex] (1)
[tex]-5\cdot m + b = -7[/tex] (2)
The solution of the system of equations is:
[tex]m = 1[/tex], [tex]b = -2[/tex]
The second line is represented by [tex]y = x-2[/tex]. And the resulting system of equations is:
[tex]0.5\cdot x -y = 0[/tex] (3)
[tex]x-y = 2[/tex] (4)
The soltuion to the system of equations is:
[tex]x = 4[/tex], [tex]y = 2[/tex]
The solution to the system of equations is x = 4 and y = 2.
Question 16
7 pts
16. The ratio of the number of girls to the number of
boys in art in 7 to 4. There are 60 boys in art. How
many girls are in art? (6.4B)
Answer:
105 girls
Step-by-step explanation:
girls : boys
7 : 4
Let total number of people in art be (7 + 4)x.
4x = 60
x = 15
no. of girls = 7x = 7 x 15 = 105
This is a question on ratios and proportions. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Write the equation of a line through (0,2) that is parallel to the graph
Answer:
y=3x+2
Step-by-step explanation:
Refer to the picture that given :)
Please help i am confused on this too!
Answer:
the first, third, and the forth
Identify the independent and dependent variable for the given situation. D = 5t
Answer:
d = dependant; t = independant
Step-by-step explanation:
The d value is dependant on the t value, therefore it is the dependant. The t is the only valuable that can be changed in the equation, therefore being the independant.
Answer:
[tex]D[/tex] = dependent; [tex]t[/tex] = independent
Step-by-step explanation:
[tex]D[/tex] is the independent variable since its value relies/depends on the value of [tex]t[/tex].
[tex]t[/tex] is the independent variable since it is the input variable which can be changed.
Hope this helps :)
Is the following relation a function, yes or no?
{(-3,4),(3,1),(5,7), (8,9), (10, 12)}
yes
no
The function rule is that each input (x value in (x,y)) should only equal to one output and one output (y value) can have more than one input.
✯the following is a function, so yes.
Answer:
yes
Step-by-step explanation:
what is the value of x for the equation: x/3+x=x/6-1
Answer:
I think the answer may be
X=2
Step-by-step explanation:
x÷3+x=x÷6-1
Add the common factors together to get
2x÷3=x÷6-1
subtract on the right side to get
2x÷3=x÷5
subtract 3 from both sides to get
2x=x÷2
subtract x from both sides to get
1x=2
pls help me its also easy
Answer:
C
Step-by-step explanation:
Ferdinand's equipment is higher than Rachel's equipment.
3. Write an equation in point-slope form that describes the line with a slope of 2 that contains the point (4,-3)?
Answer:
y + 3 = 2 (x - 4)
Step-by-step explanation:
y - y₁ = m (x - x₁)
substitute (4, -3) in for (x₁, y₁)
y - (-3) = m (x - 4)
substitute the slope (2) in for m (m=slope) and simplify (y - (-3)) to (y +3) because subtracting a negative is the same as adding a positive
y + 3 = 2 (x - 4)
and that's your final answer! hope this helped :)
My book is 79 pages. I have been reading 10 pages each day. There are 9 pages left to read. How many days have I been reading the book? Draw a model to show your thinking. Justify your answer.
Answer:
7 days
Step-by-step explanation:
If there are 9 pages left, that means you have already read 70 pages.
Since you read 10 pages a day, we can find how many days you have been reading the book by dividing 70 by 10:
70/10
= 7
This means you have been reading the book for 7 days
Answer:
7 days
Step-by-step explanation:
With 9 pages left take 79-9 to get 70 pages.
70 pages at 10 pages a day is 70/10 and you get 7 or 7 days.
i will give brainliest if correct answer
4w-24≤-12
4w≤12
w≤3
the answer i got is fifth first
SOMEONE HELP ME PLZ :)
I’ll make you the brainliest
Answer:
I think its e
Step-by-step explanation:
what is the measure of <x
Answer:
x = 104°
Step-by-step explanation:
180-76=104
z = 104°
z and x are vertical from each other, therefore, z = x
2. What is the value of 9x – 4y if x = 3 and y = 2?
F. 12.
G. 19
H. 93
1. 27
H
Answer:
G. 19 is your answer dear
Step-by-step explanation:
9(3)-4(2)
27-8 = 19
Write the equation in slope-intercept form y−6=−2/5(x−10)
Answer: y = -2/5x + 10
Step-by-step explanation:
y − 6 = − 2/5 (x − 10)
do distributive property
y - 6 = -2/5x + 4
add six to both sides
y = -2/5x + 10
boom the answer :v
The measures of the angles of a triangle are shown in the figure below
Answer:
they very much are there
Step-by-step explanation:
Answer:
37.5 degrees
Step-by-step explanation:
All triangle angles must sum up to 180 degrees
63 + 90 = 153
153 = 4x + 3
150 = 4x
37.5 = x
What will be the coordinates of point M of the image after the rotation?
0 (-4, 1)
0 (-1,4)
O (1-4)
O (4,1)
Geometry 2. Congruent triangles
Answer:
pq =28
Step-by-step explanation:
you set up the equation by making them equal each other 3x+4= 5x-12 and solve From there
PLS SQDANCEFAN. PLEASE SHOW ALL WORK!!! A bag contains 27 coins, all of which are either quarters or dimes. If their total value is $5.55, how many quarters and how many dimes are there?
I WILL MARK BRAINLIEST!!!!!!
Answer:
There are 19 quarters and 8 dimes.
Step-by-step explanation:
We will let x denote the amount of quarters.
Since there are 27 coins in total, (27-x) will be the amount of dimes there are.
Since each quarter is worth $0.25, the total value of quarters is given by 0.25x.
And since each dime is worth $0.10, the total value of dimes is given by 0.1(27-x).
We know that the total value of all 27 coins is $5.55. So, we can write the following equation:
[tex]0.25x+0.1(27-x)=5.55[/tex]
So, we will determine the value of x, the amount of quarters there are.
First, let’s multiply everything by 100 to remove the decimals. So:
[tex]100(0.25x+0.1(27-x))=100(5.55)[/tex]
Distribute:
[tex]25x+10(27-x)=555[/tex]
Distribute:
[tex]25x+270-10x=555[/tex]
Combine like terms:
[tex]15x+270=555[/tex]
Subtract 270 from both sides:
[tex]15x=285[/tex]
Divide both sides by 15:
[tex]x=19[/tex]
So, the value of x is 19.
This means that there are 19 quarters.
So, the amount of dimes must be 27-19 or 8 dimes.
9514 1404 393
Answer:
19 quarters8 dimesStep-by-step explanation:
When working mixture problems, it can be convenient to write a single equation using the variable to represent the highest-value contributor to the total value.
Here, we can let q represent the number of quarters. Then the number of dimes is 27-q.
The total value (in cents) is ...
25q +10(27 -q) = 555
15q +270 = 555 . . . . . . . collect terms
15q = 285 . . . . . . . . . subtract 270
q = 19 . . . . . . . . divide by 15
27 -19 = 8 . . . . . the number of dimes
There are 19 quarters and 8 dimes.
_____
Check
19 quarters have a value of 19×$0.25 = $4.75
8 dimes have a value of 8×$0.10 = $0.80
Then the total value of the 27 coins is $4.75 +0.80 = $5.55
_____
Additional comment
This is equivalent to working the problem by substitution where you write two equations ...
d + q = 2710d +25q = 555Then solve for d and substitute, leaving the variable q.
d = 27 -q
10(27-q) +25q = 555 . . . . the equation we wrote above
Of course, this pair of equations can be solved any convenient way, including elimination, matrix methods, and graphing.
You will find that if you eliminate the 'q' variable, you may end up dealing with negative coefficients in the equation. That is why I prefer to keep 'q' and eliminate 'd'.
What are the greatest common factor of 9a^b and 30ab^3?
Answer: 3ab IF a^b does NOT mean a to the power of b!
I believe you mean 9a²b and 30ab³
If you really mean 9aᵇ and 30ab³, then the GCF is 3a.
Step-by-step explanation:
the factors of 9 are 3*3 The factors of 30 are 2*3*5.
The only common factor of 9 and 30 is 3
a is a common factor of a and a²
b is a common factor of b and b³
Question is in image
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]y = - \frac{1}{4} x + 4 \\ [/tex]
Multiply sides by 4
[tex]4 \times y = 4 \times ( - \frac{1}{4} x + 4) \\ [/tex]
[tex]4y = 4 \times ( - \frac{1}{4} x) + 4 \times 4 \\ [/tex]
[tex]4y = - x + 16[/tex]
Add sides x
[tex] + x + 4y = + x - x + 16[/tex]
[tex]x + 4y = 16[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is (( C )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Match each expression to correct number line model.
I NEED THIS RIGHT AWAY!
(no one answered my last one so i hope this gets answered quick.)
She dove 75 feet under the sea
Please help
f(x)=1 - 2x g(x)= -x0 h(x)= x + 1
) Find the value of
(i) gf2),
Answer(a)(i)
[2]
Answer:
we get [tex]\mathbf{gf(2)=-\frac{1}{3}}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x)=1-2x\\g(x)= \frac{1}{x}\\h(x)=x^3+1[/tex]
We need to find value of [tex]gf(2)[/tex]
[tex]gf(2)=g(f(2))[/tex]
First putting f(x) inside of g(x) and then putting x=2
[tex]gf(x)=g(f(x))\\gf(x)=\frac{1}{1-2x}[/tex]
Now putting x=2 to find [tex]gf(2)[/tex]
[tex]gf(x)=\frac{1}{1-2x}\\gf(2)=\frac{1}{1-2(2)}\\gf(2)=\frac{1}{1-4}\\gf(2)=\frac{1}{-3}\\gf(2)=-\frac{1}{3}[/tex]
So, we get [tex]\mathbf{gf(2)=-\frac{1}{3}}[/tex]
Which unit would be most appropriate to measure the
width of the basement of a house?
A centimeters B meters C millimeters D kilometers
Answer:
measure the length of the area.and the width of the area. using feet
PLS HELP!!!
PLS FIND 13 and 15!!
Answer:
hi how are you doing
Step-by-step explanation:
Solve for n
8-n-4
PLZ help
YO I NEED HELP ON THIS I SUCK AT MATH!!!!!!!
Answer:
12$ per lawn mowed
Step-by-step explanation:
Which of the sets of ordered pairs represents a function?
P = {(3, 5), (−1, 5), (4, −6), (2, 9)}
Q = {(7, −2), (5, 9), (−1, 8), (5, −3)}
Answer:
P
Step-by-step explanation:
P tells us that the Domain: 3,-1,4,2 doesn't repeat
Q does repeat its Domain: 7,5,-1,5
Reminder that in order for a line of ordered pairs to be a function the domain number Shouldn't repeat, That doesn't mean that the range cant repeat.
Example: (5,-3), (5,9) Not a function
(-1,-6), (7,-6) Function
Out of the two set given, the set of ordered pairs that represents a function is: P = {(3, 5), (−1, 5), (4, −6), (2, 9)}.
What is a Function?A set of ordered pairs that has one exact y-value assigned to each x-value is considered a function.
In set P, all x-values has exactly one y-value, while in set P, the x-value, 5, has two different y-values, 9 and -3.
Therefore, the set of ordered pairs that represents a function is: set P.
Learn more about a function on:
https://brainly.com/question/10439235
#SPJ2
A store sells ice cream with assorted toppings. They charge $3.00 for an ice cream, plus 50 cents per ounce of toppings.
How much does an ice cream cost with 4 ounces of toppings?-------()
How much does an ice cream cost with 11 ounces of toppings?----()
If Elena's ice cream cost $3.50 more than Jada's ice cream, how much more did Elena's toppings weigh?-------()
Answer:
1st question: $2.00 2nd question: $5.50 3rd question: 7 oz.
Step-by-step explanation:
4 x 50= 2 = $2.00
11 x 50= 550 = $5.50
7 x 50= 350 = $3.50